Tensile strain rate, practical

If the practical tensile strain is defined as e = L/Lo 1. where L and Lq are the stretched and unstretched lengths respectively, the practical tensile strain rate is (1 /Lo)dL/dt (cf. equation 60 of Chapter 3), and a constant e can be achieved by pulling the clamps apart at a constant rate. However, if the elongational strain rate is defined as the ratio of the velocity of a material point to its displacement, this quantity, denoted ci, is ( /L)dL/dt and it will remain constant only if the clamps are pulled apart at a rate which increases exponentially with time. Several instruments which accomplish this have been described. oo-io2a Qf... 

PP bead foams were subjected to oblique impacts (167), in which the material was compressed and sheared. This strain combination could occur when a cycle helmet hit a road surface. The results were compared with simple shear tests at low strain rates and to uniaxial compressive tests at impact strain rates. The observed shear hardening was greatest when there was no imposed density increase and practically zero when the angle of impact was less than 15 degrees. The shear hardening appeared to be a unique function of the main tensile extension ratio and was a polymer contribution, whereas the volumetric hardening was due to the isothermal compression of the cell gas. Eoam material models for FEA needed to be reformulated to consider the physics of the hardening mechanisms, so their... 

In practice, since we are only interested in an estimate of the effect, we resort to an approximate analysis in which the relevant chemical potentials and mass flux, and attendant strain rate are all evaluated heuristically. The argument begins with reference to fig. 11.6 with the claim that the vacancy formation energy for the faces subjected to tensile stresses differs from that on the faces subjected to compressive stresses. Again, a rigorous analysis of this effect would require a detailed calculation either of the elastic state of the crystal or an appeal to atomistic considerations. We circumvent such an analysis by asserting that the vacancy concentrations are given by... 

In most treatises,"- 3 the strain tensor is defined with all components smaller by a factor of 2 than inequation 3, so that 711 = dui/dxi and 721 = du2/bx + bui/bx ). However, such a definition makes discussion of shear or shear flow somewhat clumsy either a practical shear strain and practical shear rate must be introduced which are twice 721 and 721 respectively, or else a factor of 2 must be carried in the constitutive equations. Since most of the discussion in this book is concerned with shear deformations, we use the definition of equation 3 which follows Bird and his school" and Lodge. - This does cause a slight inconvenience in the discussion of compressive and tensile strain, where a practical measure of strain is subsequently introduced (Section F below). In older treatises on elasticity, strains are defined without the factor of 2 appearing in the diagonal components of equation 3, but with the other components the same. 

Material functions must however be considered with respect to the mode of deformation and whether the applied strain is constant or not in time. Two simple modes of deformation can be considered simple shear and uniaxial extension. When the applied strain (or strain rate) is constant, then one considers steady material functions, e.g. q(y,T) or ri (e,T), respectively the shear and extensional viscosity functions. When the strain (purposely) varies with time, the only material functions that can realistically be considered from an experimental point of view are the so-called dynamic functions, e.g. G ((D,y,T) and ri (a), y,T) or E (o),y,T) and qg(o),y, T) where the complex modulus G (and its associated complex viscosity T] ) specifically refers to shear deformation, whilst E and stand for tensile deformation. It is worth noting here that shear and tensile dynamic deformations can be applied to solid systems with currently available instruments, whUst in the case of molten or fluid systems, only shear dynamic deformation can practically be experimented. There are indeed experimental and instrumental contingencies that severely limit the study of polymer materials in the conditions of nonlinear viscoelasticity, relevant to processing. 

Extensional flows yield information about rheological behavior that cannot be inferred from shear flow data. The test most widely used is start-up of steady, uniaxial extension. It is common practice to compare the transient tensile stress with the response predicted by the Boltzmann superposition principle using the linear relaxation spectrum a nonlinear response should approach this curve at short times or low strain rates. A transient response that rises significantly above this curve is said to reflect strain-hardening behavior, while a material whose stress falls... 

A series of six stress-strain cycles with a crosshead rate of 600 mm/min was applied to specimens having a parallel length of 25 mm and a cross-section of 1 x 4 mm2 on a tensile testing machine. The samples were continuously stretched in six hysteresis cycles up to 60% of their elongation at break values, as shown in Fig. 47. This procedure is an established one and widely practiced for elastomeric composites reinforced with fillers such as carbon black and silica, which tend to build a strong filler-filler network [83]. 

Cyclic tests provide the best representation of the conditions to which sealants are subjected in practice. They are very complex tests, however, and can be designed satisfactorily only if the material properties are well known from the results of tests using simpler loading patterns and if the rates are related to those of actual joints. Tensile extension at constant rate, stress relaxation under constant strain, and creep under constant stress are three of the simpler tests used to obtain the material properties of polymers. Tensile extension is not the simplest of the three tests (of the four basic variables only temperature can be kept constant), but it has been chosen because it is this type of loading that occurs in the sealant in a joint when the chance of failure is most probable. There is less likelihood of failure when the sealant is compressed in summer than when it is extended in winter. In addition, the tensile test is the least time-consuming and most laboratories are equipped for it. 

The data derived from stress-strain measnrements on thermoplastics are important from a practical viewpoint, providing as they do, information on the modulus, the brittleness, and the ultimate and yield strengths of the polymer. By subjecting the specimen to a tensile force applied at a uniform rate and measuring the resulting deformation, a curve of the type shown in Figure 13.15 can be constructed. 

Using this relation one can now determine the stress-strain curve at a certain reference temperature even for deformation rates that are too low to be achievable in practice in the tensile test experiment. For this purpose the tensile test is carried out at a deformation rate as low as technically possible and at a corresponding high temperature. Deformation rates and temperatures will be selected in such a way that Eq. 4.10 is fulfilled. 

Rapid strain-induced crystallization has been associated with the outstanding mechanical properties characteristic of crosslinked NR compared to its synthetic analogue, i.e. crosslinked IR. This may be due in part to a reinforcing effect of strain-induced crystals on the properties of NR as a filler or physical crosslinking junctions. In fact, tensile and tear strengths of crosslinked NR are practically higher than those of crosslinked IR, at the high-speed limit of the tear test." Therefore, it is important to control the rate of crystallization, in order to control the mechanical properties of not only NR itself, but also the NR blends. 

---